March
8, 2002
Mark
Peterson Sheds New Light on Discovery by Galileo
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Photo: Fred Leblanc
Mark
Peterson, professor of mathematics and statistics and physics,
shows the version of Dante's Inferno that Galileo defended
in his lectures to the Florentine Academy. Dante soon realized
that he had made a major blunder in arguing that the Earth's
crust would be thick enough to support its own weight as
the Inferno's roof.
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How did the politics
of the sixteenth-century Florentine court, conflicting theories
about the shape and dimensions of poet Dante Alighieri's (1265-1321)
famous vision of hell, and a mistake that threatened to bring
down a rising academic star come together to bring about a seminal
discovery in mathematical physics? Mark Peterson weaves the strands
together in a recent paper based on a new interpretation of two
obscure lectures by renowned philosopher and mathematician Galileo
Galilei (1564-1642).
Peterson, MHC professor
of mathematics and statistics and physics, said Galileo made one
of his best-known contributions to science with his discovery
of scaling laws, work that established some of the most basic
ideas in modern physics. Galileo discovered that mathematical
rules govern the scaling of objects, and that objects would collapse
under their own weight if they were simply scaled up from smaller
models. What led Galileo down this path? Peterson, in a paper
to be published in the American Journal of Physics, argues that
the answer lies quite clearly in two flawed lectures Galileo delivered
at the Florentine Academy.
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Dante
Alighieri
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Galileo
Galilei
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Galileo was a twenty-four-year-old
medical school dropout when he secured an invitation to deliver
the lectures, which were also his audition for a professorship
in mathematics at the University of Pisa. Shrewdly, Galileo chose
to speak about Dante and two competing theories about the geometry
of his Inferno.
Galileo took the side
of Antonio Manetti, a deceased member of the Florentine Academy,
and ridiculed the theories of his rival, a non-Florentine named
Alessandro Vellutello. Manetti contended that Dante's Inferno
was a cone-shaped section of the Earth, with its point at the
core and the Earth's crust as its roof, while Vellutello argued
for a much smaller cone buried deep beneath the surface.
Galileo's strategy
was brilliant, and won him the job. Intellectuals of the time
frequently got ahead by successfully attacking the work of someone
more prominent, and Galileo gained increased stature by defending
the honor of a Florentine against an attack by a non-Florentine.
But his argument that Manetti's Inferno could support itself against
collapse contained an interesting flaw: he argued that a small-scale
model of Manetti's Inferno would support itself. That much was
true. But the full-size Inferno would be too weak by an enormous
factor, and would in fact collapse.
"When Galileo
realized his mistake, probably just a short time later, it must
have struck him like a lightning bolt," Peterson said. "We
need look no further to know why the problem of scaling and the
strength of materials had urgent meaning for Galileo. He had made
a gigantic blunder in the Inferno lectures, sufficient to turn
his whole argument on its head, and with it his claim to be an
intellectual champion of his country and his sovereign, on whom
his young career depended. No one else noticed the mistake, actually,
throughout his life, but he realized that someone at any moment
could use it against him in a public way. So he had to have a
comeback."
What to do? Galileo
chose to develop the most rigorous explanation of the flaws of
his own position, a kind of "secret weapon" to be used
if he came under attack. Naturally, because he would not have
wanted to point out his own mistake, and because there was not
a scientific community to share his ideas with, Galileo kept his
theory to himself until his publication, late in life, of the
revolutionary Two New Sciences.
It was through his
blunder, Peterson argues, that Galileo developed "something
truly new, worthy of comparison with Archimedes, something that
validated his faith in geometry and hinted at undreamed of successes
to come." Peterson's own discovery came as he read the lectures
after translating them from the original Italian for a class he
teaches on Galileo (Physics 102).
"It seems a fine
irony that the first success of Galileo's mathematical physics,
which is close to being the first success of mathematical physics
at all, was a response to a problem that was not physical, but
rather the collapse of an imaginary structure in a work of literature,"
Peterson says.
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